I up grew up using cast iron pans, griddles and muffin pans, so everything I know is passed down.

Did you get it good and seasoned yet? I LOVE my griddle, use it daily, great for burritos, quesadillas, grilled cheeses, paninis, pancakes yes yes!

For cleaning the griddle, I simply wash it off with water after it cools off then pop it back on a warm burner until dry, apply oil if needed. Sometimes if I forget to wash it after cooking, I just heat it up next time I'm ready to cook and when it's hot take a wet paper towel and run it all over the griddle with a spatula. Then it's super clean.

For pans, if they need serious scraping, like you cooked eggs and they are stuck on, put an inch of water in the pan and heat up on the stove until it softens. Then take to the sink and should scrub right out with nylon scrubbie, cloth or brush. Oil it and place back on the hot burner til dry.

Rust is the enemy, not water per se, we have ALWAYS cleaned with water, the key is heating is back up again when it's clean so it dries. I have pans that are 20+ years old. I use soap too when needed, but rarely, I just oil afterwards and heat for sure, in case of any stripping.

And if you ever get gnarly build up, pop it in a hot oven a few hours or throw it in your backyard fire pit or BBQ grill to bake off some of the build up. Beware of baking off all the good bits though.